Using the coupled cluster method for high orders of approximation and Lanczos exact diagonalization we study the ground-state phase diagram of a quantum spin-1/2 J1-J2 model on the square lattice with plaquette structure. We consider antiferromagnetic (J1 > 0) as well as ferromagnetic (J1 < 0) nearest-neighbor interactions together with frustrating antiferromagnetic next-nearestneighbor interaction J2 > 0. The strength of inter-plaquette interaction λ varies between λ = 1 (that corresponds to the uniform J1-J2 model) and λ = 0 (that corresponds to isolated frustrated 4-spin plaquettes). While on the classical level (s → ∞) both versions of models (i.e., with ferroand antiferromagnetic J1) exhibit the same ground-state behavior, the ground-state phase diagram differs basically for the quantum case s = 1/2. For the antiferromagnetic case (J1 > 0) Néel antiferromagnetic long-range order at small J2/J1 and λ 0.47 as well as collinear striped antiferromagnetic long-range order at large J2/J1 and λ 0.30 appear which correspond to their classical counterparts. Both semi-classical magnetic phases are separated by a nonmagnetic quantum paramagnetic phase. The parameter region, where this nonmagnetic phase exists, increases with decreasing of λ. For the ferromagnetic case (J1 < 0) we have the trivial ferromagnetic ground state at small J2/|J1|. By increasing of J2 this classical phase gives way for a semi-classical plaquette phase, where the plaquette block spins of length s = 2 are antiferromagnetically long-range ordered. Further increasing of J2 then yields collinear striped antiferromagnetic long-range order for λ 0.38, but a nonmagnetic quantum paramagnetic phase λ 0.38.
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